Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions

Authors:
L. C. Ceng;J. C. Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, PR China;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, ROC
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 7
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Abstract

The purpose of this paper is to investigate the convergence of general approximate proximal algorithm (resp. general Bregman-function-based approximate proximal algorithm) for solving the generalized variational inequality problem (for short, GVI(T,@W) where T is a multifunction). The general approximate proximal algorithm (resp. general Bregman-function-based approximate proximal algorithm) is to define new approximating subproblems on the domains @W"n@?@W, n=1,2,..., which form a general approximate proximate point scheme (resp. a general Bregman-function-based approximate proximate point scheme) for solving GVI(T,@W). It is shown that if T is either relaxed @a-pseudomonotone or pseudomonotone, then the general approximate proximal point scheme (resp. general Bregman-function-based approximate proximal point scheme) generates a sequence which converges weakly to a solution of GVI(T,@W) under quite mild conditions.